R = 6 cm ; α= 60°= π/3 r = ½R/cos30° = 2√3 cm Area of circle : A₁ = πr² = π(2√3)² = 12π cm² Area of angular sector: A₂ = ½αR² = ½ π/3 6² = 6π cm² Area of circular segment: A₃=½r²(2α-sin2α)=½(2√3)²(120°-sin120°) A₃ = 7,37022 cm² Red shaded area: A = A₁ - A₂ - 2A₃ A = 12π - 6π - 2*7,37022 A = 4,109 cm² ( Solved √ )
Concise solution to a very intricate problem! 🙂
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R = 6 cm ; α= 60°= π/3
r = ½R/cos30° = 2√3 cm
Area of circle :
A₁ = πr² = π(2√3)² = 12π cm²
Area of angular sector:
A₂ = ½αR² = ½ π/3 6² = 6π cm²
Area of circular segment:
A₃=½r²(2α-sin2α)=½(2√3)²(120°-sin120°)
A₃ = 7,37022 cm²
Red shaded area:
A = A₁ - A₂ - 2A₃
A = 12π - 6π - 2*7,37022
A = 4,109 cm² ( Solved √ )
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